# Solve using the Square Root Property 125=2x*x

125=2x⋅x
Rewrite the equation as 2x⋅x=125.
2x⋅x=125
Simplify.
Raise x to the power of 1.
2(x1x)=125
Raise x to the power of 1.
2(x1x1)=125
Use the power rule aman=am+n to combine exponents.
2×1+1=125
2×2=125
2×2=125
Divide each term by 2 and simplify.
Divide each term in 2×2=125 by 2.
2×22=1252
Cancel the common factor of 2.
Cancel the common factor.
2×22=1252
Divide x2 by 1.
x2=1252
x2=1252
x2=1252
Take the square root of both sides of the equation to eliminate the exponent on the left side.
x=±1252
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 1252 as 1252.
x=±1252
Simplify the numerator.
Rewrite 125 as 52⋅5.
Factor 25 out of 125.
x=±25(5)2
Rewrite 25 as 52.
x=±52⋅52
x=±52⋅52
Pull terms out from under the radical.
x=±552
x=±552
Multiply 552 by 22.
x=±552⋅22
Combine and simplify the denominator.
Multiply 552 and 22.
x=±55222
Raise 2 to the power of 1.
x=±55222
Raise 2 to the power of 1.
x=±55222
Use the power rule aman=am+n to combine exponents.
x=±55221+1
x=±55222
Rewrite 22 as 2.
Use axn=axn to rewrite 2 as 212.
x=±552(212)2
Apply the power rule and multiply exponents, (am)n=amn.
x=±552212⋅2
Combine 12 and 2.
x=±552222
Cancel the common factor of 2.
Cancel the common factor.
x=±552222
Divide 1 by 1.
x=±5522
x=±5522
Evaluate the exponent.
x=±5522
x=±5522
x=±5522
Simplify the numerator.
Combine using the product rule for radicals.
x=±52⋅52
Multiply 2 by 5.
x=±5102
x=±5102
x=±5102
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
x=5102
Next, use the negative value of the ± to find the second solution.
x=-5102
The complete solution is the result of both the positive and negative portions of the solution.
x=5102,-5102
x=5102,-5102
x=5102,-5102
The result can be shown in multiple forms.
Exact Form:
x=5102,-5102
Decimal Form:
x=7.90569415…,-7.90569415…
Solve using the Square Root Property 125=2x*x